Polymers polarization propagator

Polarization propagator for computing the polarizability per unit cell of polymers... 

POLARIZATION PROPAGATOR FOR COMPUTING THE POLARIZABILITY PER UNIT CELL OF POLYMERS... 

In the case of crystalline polymers it may be that solvents can cause cracking by activity in the amorphous zone. Examples of this are benzene and toluene with polyethylene. In polyethylene, however, the greater problem is that known as environmental stress cracking , which occurs with materials such as soap, alcohols, surfactants and silicone oils. Many of these are highly polar materials which cause no swelling but are simply absorbed either into or on to the polymer. This appears to weaken the surface and allows cracks to propagate from minute flaws. 

The authors concluded that the side reactions normally observed in amine-initiated NCA polymerizations are simply a consequence of impurities. Since the main side reactions in these polymerizations do not involve reaction with adventitious impurities such as water, but instead reactions with monomer, solvent, or polymer (i.e., termination by reaction of the amine-end with an ester side chain, attack of DMF by the amine-end, or chain transfer to monomer) [11, 12], this conclusion does not seem to be well justified. It is likely that the role of impurities (e.g., water) in these polymerizations is very complex. A possible explanation for the polymerization control observed under high vacuum is that the impurities act to catalyze side reactions with monomer, polymer, or solvent. In this scenario, it is reasonable to speculate that polar species such as water can bind to monomers or the propagating chain-end and thus influence their reactivity. 

Ionic chain polymerisations refer to chain mechanisms in the course of which the propagation step consists of the insertion of a monomer into an ionic bond. The strength of this ionic bond can vary, depending on the nature of the species, the temperature and the polarity of the solvent, between a closed ionic pair in contact up to free ions (see Figure 23). Final polymer microstructure (configuration,...) and molecular mass distribution depend on the actual nature of the active ionic species. 

The propagation for cyclic formals also involves a solvated oxonium ion and a highly polar monomer [10, 12]. Since under optimum conditions the polymers are essentially free from any kind of end-group (except very small amounts of -OH) Plesch and Westermann [36, 37] concluded that they must be formed by a ring-expansion mechanism, involving a 4-centred transition state ... 

The reason is that these alleged kp values are mostly composite, comprising the rate constants of propagation of uncomplexed Pn+, paired Pn+ (Pn+A ), and Pn+ complexed with monomer or polymer or both, without or with an associated A" [17]. Even when we will eventually have genuine kp values for solvents other than PhN02, it will not be possible to draw many (or any ) very firm conclusions because the only theoretical treatments of the variation of rate constants with solvent polarity for (ion + molecule) reactions are concerned with spherically symmetrical ions, and the charge distribution in the cations of concern to us is anything but spherically symmetrical. 

Polymerisations of undiluted, bulk monomer are rare except for those initiated by ionising radiations and they require a special treatment which will be given later. The most common situation is to have the propagating ions in a mixture of monomer and solvent, and as the solvation by the solvent is ubiquitous and may dominate over that by other components of the reaction mixture, mainly because of the mass-action effect, it will not be noted by any special symbol, except in a few instances. This means that we adopt the convention that the symbol Pn+ denotes a growing cation solvated mainly by the solvent correspondingly kp+ denotes the propagation constant of this species, subject to the proviso at the end of Section 2.3. Its relative abundance depends upon the abundance of the various other species in which the role of the solvent as the primary solvator has been taken over by any or all of the anion or the monomer or the polymer. The extent to which this happens depends on the ionic strength (essentially the concentration of the ions), and the polarity of the solvent, the monomer and the polymer, and their concentrations. 

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